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Who Cites addprime?
addprimeDef (t)' == term_iterate(x.x';x.x';op.op;f.f;P.trace(P);a,b. a b;t)
Thm* t:Term. (t)' Term
tapp Def t1 t2 == tree_node( < t1, t2 > )
Thm* t1,t2:Term. t1 t2 Term
ttrace Def trace(l) == tree_leaf(ts_trace(l))
Thm* l:Label. trace(l) Term
tfvar Def l == tree_leaf(ts_fvar(l))
Thm* l:Label. l Term
topr Def f == tree_leaf(ts_op(f))
Thm* f:Label. f Term
tpvar Def l' == tree_leaf(ts_pvar(l))
Thm* l:Label. l' Term
term_iterate Def term_iterate(v;p;op;f;tr;a;t) == t_iterate(x.ts_case(x)var(a)= > v(a)var'(b)= > p(b)opr(c)= > op(c)fvar(d)= > f(d)trace(P)= > tr(P)end_ts_case ;a;t)
Thm* A:Type, v,op,f,p,tr:(LabelA), a:(AAA), t:Term. term_iterate(v;p;op;f;tr;a;t) A
node Def tree_node( < x, y > ) == tree_node( < x,y > )
Thm* E:Type, x,y:Tree(E). tree_node( < x, y > ) Tree(E)
ts_trace Def ts_trace(x) == inr(inr(inr(inr(x))))
Thm* x:Label. ts_trace(x) ts()
tree_leaf Def tree_leaf(x) == inl(x)
Thm* E,T:Type, x:E. tree_leaf(x) tree_con(E;T)
Thm* E:Type, x:E. tree_leaf(x) Tree(E)
ts_fvar Def ts_fvar(x) == inr(inr(inr(inl(x))))
Thm* x:Label. ts_fvar(x) ts()
ts_op Def ts_op(x) == inr(inr(inl(x)))
Thm* x:Label. ts_op(x) ts()
ts_pvar Def ts_pvar(x) == inr(inl(x))
Thm* x:Label. ts_pvar(x) ts()
ts_case Def ts_case(x)var(a)= > v(a)var'(b)= > p(b)opr(f)= > op(f)fvar(x)= > f(x)trace(P)= > t(P)end_ts_case == Case(x) Case ts_var(a) = > v(a) Case ts_pvar(b) = > p(b) Case ts_op(f) = > op(f) Case ts_fvar(x) = > f(x) Case ts_trace(P) = > t(P) Default = >
Thm* A:Type, v,op,f,p,t:(LabelA), x:ts(). ts_case(x)var(a)= > v(a)var'(b)= > p(b)opr(f)= > op(f)fvar(y)= > f(y)trace(P)= > t(P)end_ts_case A
t_iterate Def t_iterate(l;n;t) == Case(t) Case x;y = > n(t_iterate(l;n;x),t_iterate(l;n;y)) Case tree_leaf(x) = > l(x) Default = > True (recursive)
Thm* E,A:Type, l:(EA), n:(AAA), t:Tree(E). t_iterate(l;n;t) A
tree_node Def tree_node(x) == inr(x)
Thm* E,T:Type, x:(TT). tree_node(x) tree_con(E;T)
Thm* E:Type, x,y:Tree(E). tree_node( < x,y > ) Tree(E)
case_default Def Default = > body(value,value) == body
case_ts_trace Def Case ts_trace(x) = > body(x) cont(x1,z) == (x1.inr(x2) = > (x1.inr(x2) = > (x1.inr(x2) = > (x1.inr(x2) = > body(hd([x2 / tl(x1)])) cont(hd(x1),z))([x2 / tl(x1)]) cont(hd(x1),z))([x2 / tl(x1)]) cont(hd(x1),z))([x2 / tl(x1)]) cont(hd(x1),z))([x1])
case_ts_fvar Def Case ts_fvar(x) = > body(x) cont(x1,z) == (x1.inr(x2) = > (x1.inr(x2) = > (x1.inr(x2) = > (x1.inl(x2) = > body(hd([x2 / tl(x1)])) cont(hd(x1),z))([x2 / tl(x1)]) cont(hd(x1),z))([x2 / tl(x1)]) cont(hd(x1),z))([x2 / tl(x1)]) cont(hd(x1),z))([x1])
case_ts_op Def Case ts_op(x) = > body(x) cont(x1,z) == (x1.inr(x2) = > (x1.inr(x2) = > (x1.inl(x2) = > body(hd([x2 / tl(x1)])) cont(hd(x1),z))([x2 / tl(x1)]) cont(hd(x1),z))([x2 / tl(x1)]) cont(hd(x1),z))([x1])
case_ts_pvar Def Case ts_pvar(x) = > body(x) cont(x1,z) == (x1.inr(x2) = > (x1.inl(x2) = > body(hd([x2 / tl(x1)])) cont(hd(x1),z))([x2 / tl(x1)]) cont(hd(x1),z))([x1])
case_ts_var Def Case ts_var(x) = > body(x) cont(x1,z) == InjCase(x1; x2. body(x2); _. cont(z,z))
case Def Case(value) body == body(value,value)
case_tree_leaf Def Case tree_leaf(x) = > body(x) cont(x1,z) == InjCase(x1; x2. body(x2); _. cont(z,z))
case_node Def Case x;y = > body(x;y) cont(x1,z) == InjCase(x1; _. cont(z,z); x2. x2/x3,x2@0. body(x3;x2@0))
hd Def hd(l) == Case of l; nil "?" ; h.t h
Thm* A:Type, l:A List. ||l||1 hd(l) A
Thm* A:Type, l:A List. hd(l) A
tl Def tl(l) == Case of l; nil nil ; h.t t
Thm* A:Type, l:A List. tl(l) A List
case_inr Def inr(x) = > body(x) cont(value,contvalue) == InjCase(value; _. cont(contvalue,contvalue); x. body(x))
case_inl Def inl(x) = > body(x) cont(value,contvalue) == InjCase(value; x. body(x); _. cont(contvalue,contvalue))

Syntax:(t)' has structure: addprime(t)

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